She briefly attended Bristol Grammar School until the family moved to Wichita, Kansas (U.S.) in 2013 due to her father's job in the oil industry.

[3] In 2014, Swan was a member of the four-strong GB squad, coached by Judy Murray, that triumphed in the Maureen Connolly Challenge Trophy, an annual under-18s competition, against the U.S.

[8][9] On 30 January 2015, Swan defeated Dalma Gálfi, after facing three match points to reach her first junior Grand Slam final at the Australian Open, which she lost 1–6, 4–6 to Tereza Mihalíková.

[6][10] In March, just before her 16th birthday, Swan achieved her first victories on the senior tour,[11] coming through the qualifying draw to win a $10k tournament in Sharm El Sheikh.

Judy Murray, captain of the British Fed Cup team, already had Swan in her plans, to represent Great Britain in 2016.

[12] In June, Swan competed at the Wimbledon qualifying tournament, after being granted a wildcard entry, beating ninth seed and 118th ranked Kristína Kučová in the first round, in straight sets.

[22] Following problems in late 2016/early 2017 from recurring injuries,[23] Swan returned at the Soho Square Future in Sharm El Sheikh, winning the $15k tournament by beating Pemra Özgen in the final, in straight sets.

[24] At the start of the year, it was announced that Swan had joined Andy Murray's "77 Sports Management" with a statement from him saying, "Katie is a player I've been watching for a while.

[27] In June, she won two rounds in qualifying at the Nottingham Open, to reach the main draw of a WTA Tour event by right for the first time, earlier appearances having relied on wildcards.

[33] Swan also had some success on the ITF Circuit, winning a $25k tournament in Orlando in February 2021, and the $25k Paf Open in Haabneeme in November.

[36] In February, she defeated Sachia Vickery at the $25k event in Santo Domingo to win her tenth title on the ITF Circuit, and sixth at $25k level.

[45] Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.